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For a certain distribution, the measurement 12.1 is 1.5

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For a certain distribution, the measurement 12.1 is 1.5 [#permalink] New post 01 Jul 2016, 18:32
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66% (01:53) correct 33% (02:51) wrong based on 24 sessions
For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the measurement 17.5 is 3.0 standard deviations above the mean. What is the mean of the distribution?

A. 13.8
B. 13.9
C. 14.0
D. 14.1
E. 14.2


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Question: 12
Page: 121
[Reveal] Spoiler: OA

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Re: For a certain distribution, the measurement 12.1 is 1.5 [#permalink] New post 01 Jul 2016, 21:43
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The distance between 12.1 and 17.5 is 5.4. The SD between them = 3.0+1.5 = 4.5 => one SD is 5.4 /4.5 = 1.2
Now 12.1 is 1.5 SD away from mean => the mean = 12.1+1.5*1.2 = 13.9
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Re: For a certain distribution, the measurement 12.1 is 1.5 [#permalink] New post 02 Jul 2016, 06:12
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sandy wrote:
For a certain distribution, the measurement 12.1 is 1.5 standard deviations below the mean, and the measurement 17.5 is 3.0 standard deviations above the mean. What is the mean of the distribution?

A. 13.8
B. 13.9
C. 14.0
D. 14.1
E. 14.2



Another approach:

Let M = the mean
Let D = standard deviation

12.1 is 1.5 standard deviations below the mean
So, M - 1.5D = 12.1

17.5 is 3.0 standard deviations above the mean
So, M + 3D = 17.5

We have the system:
M - 1.5D = 12.1
M + 3D = 17.5

Multiple both sides of the top equation by 2 to get:
2M - 3D = 24.2
M + 3D = 17.5

ADD the two equations to get: 3M = 41.7
Solve to get: M = 13.9
Answer: B

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Brent
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Re: For a certain distribution, the measurement 12.1 is 1.5 [#permalink] New post 13 Dec 2016, 11:06
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Your first approach is extremely hard to understand!
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Re: For a certain distribution, the measurement 12.1 is 1.5 [#permalink] New post 25 Jan 2018, 01:26
2nd approach is much more simplified
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Re: For a certain distribution, the measurement 12.1 is 1.5 [#permalink] New post 25 Jan 2018, 01:44
Easiest way would be to plug in numbers.
Start by plugging in C (14.0):
If answer is C, SD must be: 14.0 - 12.1 = 1.9
For answer to hold we need: 14.0 - 1.5*SD = 12.1 AND 14.0 + 3*SD = 17.5
Check whether answer is correct: 1.9 equals 1.5 SD's, multiplying by 2 (2*1.5 = 3) yields 3*SD's: 1.9*2 = 3.8
Therefore if mean is 14: 14.0 + 3*SD = 17.8 -> cannot be answer and mean must be closer to 12.1
Try the same for either A to see that answer must be B or continue by plugging in B to see that answer is B (13.9)
Re: For a certain distribution, the measurement 12.1 is 1.5   [#permalink] 25 Jan 2018, 01:44
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For a certain distribution, the measurement 12.1 is 1.5

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